ABSTRACT
The multiobjective optimization problems with several conflicting objectives have been an important research topic during the last few decades. These problems arise in several areas of modern research such as in economics, game theory, optimal control, and decision theory. Many authors have developed necessary and sufficient conditions for multiobjective optimization problems. See for example, Kuhn and Tucker [151], Arrow et al. [7], Da Cunha and Polak [59], and Tanino and Sawaragi [269]. Singh [255] established necessary conditions for Pareto optimality by using the concept of convergence of a vector at a point and Motzkin’s theorem of alternative and obtained several sufficient optimality conditions under the assumptions of pseudoconvexity and quasiconvexity on the functions involved. Chew and Choo [47] established the necessary and sufficient optimality conditions for multiobjective pseudolinear programming problems. Bector et al. [20] derived several duality results for the Mond-Weir type dual of a multiobjective pseudolinear programming problem and studied its applications to certain multiobjective fractional programming problems. Recently, various generalizations of the notion of convexity have been introduced to obtain optimality conditions and duality theorems for differentiable multiobjective optimization problems. For further details, we refer to Kaul and Kaur [137], Preda [224], and Hachimi and Aghezzaf [97].
